We have developed a modified version of the Iterative Blind Deconvolution (IBD) algorithm of Lane, applicable to different types of astronomical data. Besides using positivity, convolution, and support constraints, we have also applied band-limit, multiple image, and Fourier modulus constraints. By using all the available image constraining information, we are able to successfully recover object and point spread function information from noisy data. The algorithm's performance under controlled conditions using simulated data for a binary source object, a compact multiple quasi-point source object, and an extended object with low contrast are demonstrated. The ability of the algorithm to restore information beyond the conventional cutoff frequency is also demonstrated. Results are presented for infrared speckle imaging of (1) the nearby binary star Gl 914, which resolves the secondary component into two stars, and (2) the asteroid 4 Vesta. We also present results for "direct" imaging data in the form of a visible high-resolution image of Capella and an infrared adaptively corrected image of the Galactic center.